Why do we need an operation like this in a mechanical brain? Among other reasons, what we want to do with a number, in mathematics, often depends on its sign. It may happen that a table is, for negative arguments, the negative of what it is for positive arguments; in other words, _F_(-_x_) =-_F_(_x_). This is true, for instance, for a table of _cubes_ {_F_(_x_) = _x_³} or for a table of _trigonometric tangents_ (see Supplement 2). If so, we certainly do not want to take the time and trouble to list the whole table. We put down only half the table and then, if _x_ is negative, use the negative of the value in the table. In order to apply such a time-saving rule when using the machine, we need the selection counter or its equivalent. Checking There is another special counter in the machine that is called the _check counter_. It also has all the properties of an ordinary storage counter and, in addition, one extra property: If the sign of the number stored in the check counter on a certain coding line is negative, then on the next coding line the machine may be stopped. In other words, suppose that the check counter stores a certain tolerance _t_. Suppose, under the instructions we give the machine, that it calculates a positive number _x_ that ought to be less than this tolerance. Suppose that something may go wrong and that _x_ actually may be greater than _t_. Then we put a check into our instructions. We tell the machine: When you have found _x_, subtract it from _t_. If the result is positive, go ahead. If the result is negative or zero, _stop_! Here is the coding. Suppose that the tolerance _t_ is in switch 751. Suppose that the number _x_ to be checked is in counter 4321. Then the instructions and coding are: Clear the check counter — — 7 Put in the tolerance, from switch 751 751 74 7 Subtract the absolute value of the number to be checked 4321 74 71 Stop, O Mechanical Brain, if your result be negative! — — 64 An operation like this is very useful in a mechanical brain. It enables the calculation to be interrupted if something has gone wrong. Of course, other operations of checking besides this one are used—for example, inspecting for reasonableness the results printed on typewriter 1. Other Operations